Complex Numbers questions
967 published questions with worked solutions.
- If and are different complex numbers with | |=1 then | - 1- | is equal to
- The value of 1+i^2+i^4+i^6+ +i^ 2n is
- Let z be a complex number and a be a real parameter such that z^2+az+a^2=0, then
- If z_1 and z_2 are two nth roots of unity, then ( z_1 z_2 ) is a multiple of
- If z is a complex number, then |3z-1|=3|z-2| represents
- If the imaginary part of the expression z-1 e^ i + e^ i z-1 be zero, then the locus of z is
- 1-c^2 =nc-1 and z=e^ i , then c 2n (1+nz) (1+ nz ) is equal to
- The complex number z satisfies the condition |z- 25 z |=24. The maximum distance from the origin of coordinates to the point z is
- The number of non-zero integral solutions of the equation |1-i|^x=2^x is
- If |z+4| 3, then the greatest and the least value of |z+1| are
- Let a be a complex number such that |a|<1 and z_1,z_2, be vertices of a polygon such that z_k=1+a+a^2+ +a^ k-1 . Then the...
- Common roots of the equations z^3+2z^2+2z+1=0 and z^ 1985 +z^ 100 +1=0 are
- The equation z^5+z^4+z^3+z^2+z+1=0 is satisfied by
- Let z_1 and z_2 be two complex numbers with and as their principle arguments such that + > , then principal (z_1z_2) is given by
- If |z-2|= |z-1|,|z-5| , where z is a complex number, then
- If | z-2 z+2 |= 6, then the locus of z is
- Locus of z, if ( z-1 z+1 )= 2, is
- If iz^3+z^2-z+i=0, then |z| is equal to
- The value of i (x-i)+i^2 +i^3 (x+i)+i^4 (2 ^ -1 x ), (where x>0 and i= -1 ), is
- The region of the complex plane for which | z-a z+ a |=1 [ Re (a) 0], is
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